Place chicken in saucepan with enough cold water to cover, plus 1 inch. Bring to a simmer (do not boil) over medium heat, and simmer until chicken is cooked through or meat thermometer inserted in center reaches 170°F, about 18 minutes. Drain and cool completely.
Dice chicken and place in medium bowl. Stir in apple pieces, 4 tablespoons mayonnaise, yogurt, salt, and pepper. Spread remaining mayonnaise on toast slices.
Place lettuce leaf on bottom pieces of toast. Top with tomato, two pieces of bacon, middle pieces of toast, remaining lettuce leaves, chicken salad, and remaining pieces of toast.